Question

Question 22

Which power of 8 is equal to $2^6$?
(a) 3
(b) 2
(c) 1
(d) 4

Answer 1

Let power of 8 be x.
According to the equation,
$8^x=2^6\Rightarrow (2^3{)}^x=2^6[\because 8=2\times 2\times 2=2^3]\Rightarrow 2^{3x}=2^6[\because (a^m{)}^n=a^{m\times n}])$
Since, base are equal, then by equating their exponents, we get
$3x=6$
$\Rightarrow \frac{3x}{3}=\frac{6}{3}\Rightarrow x=2$
Hence, the power of 8 is 2, which is equal to $2^6$.